Alternating SequenceDate: 01/27/97 at 20:43:09 From: KEITH MCKENZIE Subject: I need help Dear Dr. Math, I need help. I have a problem that neither my friends nor I can get. I thought you could help. We have to find a pattern and find the next three numbers for this: 0, 8, 27, _, _, _. I hope you can find the answer. Sincerely, Shoushou Date: 01/29/97 at 16:53:47 From: Doctor Wallace Subject: Re: I need help Dear Shoushou, For this series, the first thing to notice is that all of the numbers are perfect cubes: 0 = 0^3, 8 = 2^3, and 27 = 3^3. If we list the numbers that are the cube roots of these numbers, we get this series: 0, 2, 3... Now, all you have to do is find a pattern among these three. The one I see is an alternating series. There may be others. Let me know how your work goes on this problem. -Doctor Wallace, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 01/29/97 at 18:49:05 From: KEITH MCKENZIE Subject: Re: I need help This is Shoushou. Thanks for giving me that great hint. I'm not sure if I have it right, but I think it might be +2, +1, +2, +1. This doesn't quite satisfy me, but it's the best I can come up with for now. Sincerely, Shoushou Date: 01/30/97 at 12:37:59 From: Doctor Wallace Subject: Re: I need help Dear Shoushou, I think you're right. That's what I came up with, too. And I feel the same way - I wasn't quite satisfied. Somehow, it didn't feel just right. I think it was because there were only 3 numbers given, and it's hard to come to just one pattern with only three numbers. But it seems that, since the number 1 was missing, +2 +1 +2 +1 ... is the only thing that makes sense. Then the next two numbers in the pattern would be 5^3 and 6^3. What did your teacher have in mind for the answer? If you can come up with another pattern that fits the series, please write and let me know. And write again any time you have other math questions! -Doctor Wallace, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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